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Winners: The IS 318 team on the train to the 2010 state championship in “Brooklyn Castle.” Photo: Rescued Media

The powerful new documentary “Brooklyn Castle,” about the renowned chess team of IS 318 in Williamsburg, shows how dedicated teachers can enrich the lives of disadvantaged students. It has important lessons for education reformers.

Over the past decade, the IS 318 team has won more chess championships than any school in the country. Earlier this year — after filmmakers finished production — it became the first middle school to win the national high-school championship, beating out dozens of elite public and private schools.

The film chronicles five students and the challenges they face: Justus Williams is “the LeBron James of chess;” Alexis Paredes is an immigrant striver; Patrick Johnson has ADHD and uses chess to improve his concentration and self-confidence; Rochelle Ballantyne endeavors to be the first female African-American chess master; Pobo Efekoro is the team’s emotional leader. (I met the students at a Rooftop Films screening: They’re as impressive off- as on- camera.)

Chess is embedded into the school’s curriculum. All sixth-graders take weekly chess classes and can continue with it as an elective for the next two years. There seems to be a positive impact on student achievement: 53 percent of IS 318 students are proficient in English and 71 percent in math, above city averages.

Because the unions fight so hard to protect bad apples, education reformers sometimes forget that most teachers are dedicated and hardworking. “Brooklyn Castle” offers an inspiring reminder of that fact. The heart and soul of the program is the chess teacher Elizabeth Spiegel. (In the movie, she’s Elizabeth Vicary; she has since married.)

Spiegel began teaching at IS 318 under the auspices of the nonprofit Chess-in-the-Schools. In 2006, she was hired by the school as a full-time chess teacher.

Paul Tough profiles Spiegel in his new book “How Children Succeed: Grit, Curiosity, and the Hidden Power of Character,” and she clearly inculcates those values in her students.

She sees chess as an educational tool that develops qualities like perseverance and analytical thinking. As Spiegel notes, “Teaching chess is really about teaching the habits that go along with thinking — like how to understand your mistakes and how to be more aware of your thought processes.”

(The city’s lucky enough to have several great chess programs — Hunter College and Edward R. Murrow high schools are two others. Many high-performing charter schools also teach chess, including the Success network.)

John Galvin, IS 318’s assistant principal and chess coach, is another hero. In the film, he finds a way to save the chess team when recessionary budget cuts threaten the program. He has even been known to use his personal credit card to fund trips to important tournaments.

It seems that every weekend, Spiegel and Galvin are in a hotel conference room at a tournament, exhorting their students on to victory — or, when they lose, patiently analyzing what mistakes they made.

Some of the broader lessons to be learned from “Brooklyn Castle”:

Demography Isn’t Destiny. IS 318’s students are mostly black and Latino; over 60 percent come from homes below the federal poverty line. Galvin notes: “The premise of the team is that if you work hard and study, you can be the intellectual equal of any kid in the US.”

Teachers Matter. The school’s excellent teachers validate the research that shows that teacher quality greatly impacts student achievement. Why then, do the unions seem to think teachers don’t matter much — since they spend so much effort to protect bad ones?

Character Counts. Just as important as the facts and figures taught at IS 318 are the teachers’ efforts to instill values, build character and forge good habits of mind and behavior.

Empowering Schools Works. IS 318 was able to bring on a full-time chess teacher thanks to Bloomberg-era reforms that give principals greater control over staffing and budget decisions.

Extracurricular Isn’t Extra. Each afternoon, IS 318 students participate in enriching activities like chess, robotics, botany, tennis, band and drama, but budget cuts threaten their survival. (Donations can be made via the “Brooklyn Castle” Web site.)

Katie and Nelson Dellamaggiore, who produced and directed “Brooklyn Castle,” deserve an Oscar. But the kids at IS 318 are the real winners — and, so, if we heed the important lessons they have to teach, is the whole city.

Charles Sahm is the deputy director of the Manhattan Institute’s Center for State and Local Leadership.